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    STUDIA MATHEMATICA - Issue no. 1 / 2007  
         
  Article:   A COMBINED MONTE CARLO AND QUASI-MONTE CARLO METHOD FOR ESTIMATING MULTIDIMENSIONAL INTEGRALS.

Authors:  NATALIA ROŞCA. 		 
       
         
  Abstract:  In this paper, we propose a method to estimate a multidimensional integral I. The method combines the ideas of the Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods. We call our method random sampling from non-uniform low-discrepancy sequences. The method is based on a new estimator for the integral I, for which some theoretical properties are given. A statistical as well as a deterministic analysis of the error are performed. In the statistical analysis, the accuracy is measured by constructing confidence intervals for I. In the deterministic analysis, deterministic upper bounds for the error of approximation are given. The method is applied to a numerical example. The numerical results indicate that our method performs better than the MC and QMC methods.  
         
     
         
         
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